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new methode for finding M(p) ?

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  • Norman Luhn
    Hello , I have found a relation for Mersenne primes. Perhaps is it know ?! R=(2*M(p)-2)/3=(T^2 mod M(p)) The problem is,how can I proof that exist a number T
    Message 1 of 3 , Mar 23, 2008
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      Hello , I have found a relation for Mersenne primes.
      Perhaps is it know ?!

      R=(2*M(p)-2)/3=(T^2 mod M(p))

      The problem is,how can I proof that exist a number T
      where T^2 mod M(p) = R. T is >= R

      Example:

      M(13)=8191
      R=5460
      we found T=5929

      The idea is a consequence of the Lucas Lehmer Test.


      regards

      Norman





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    • Norman Luhn
      T is not =R. We find for M(5) T=12,19 M(7) T=46,81 M(11) no T so that T^2 mod 2047 = 1364 M(13) T=2262,5929 .... N.L. Lesen Sie Ihre E-Mails jetzt einfach von
      Message 2 of 3 , Mar 23, 2008
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        T is not >=R.

        We find for
        M(5) T=12,19
        M(7) T=46,81
        M(11) no T so that T^2 mod 2047 = 1364
        M(13) T=2262,5929
        ....

        N.L.



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      • leavemsg1
        ... if R=(2*Mp-2)/3=((T^2) mod Mp), then... ... (it s a plausible idea), but if it works?? it s better than LL I can determine the exact T(sub k) to use in
        Message 3 of 3 , Mar 25, 2008
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          --- In primenumbers@yahoogroups.com, Norman Luhn <nluhn@...> wrote:
          >
          > Hello , I have found a relation for Mersenne primes.
          > Perhaps is it know(n) ?! (probably not!)
          >
          if R=(2*Mp-2)/3=((T^2) mod Mp), then...
          >
          (it's a plausible idea), but if it works?? it's better than LL

          I can determine the exact T(sub k) to use in this test.
          e.g. #1
          Suppose that Mp= 7, and p= 3;
          R = (2*7 -2)/3 =4 == ((2^2) mod 7) == 4; M3 is prime!
          T was chosen by taking R/2 = 4/2 = 2 = T(1);
          ..2.....4....6...8... and so on...
          T(1)...(2)..(3).(4)...
          where k= floor[(p+1)/2 -1] = floor[(3+1)/2 -1] = 1; p= 3 from M(3).

          e.g #2
          Suppose that Mp= 31, and p= 5;
          R = (2*31 -2)/3 =20 == ((2^12) mod 31) == 20; M5 is prime!
          T was chosen by taking R/2 = 20/2 = 10 = T(1); but k equals 2(below)
          .10...12....14... and so on...
          T(1)..(2)...(3) ...
          where k= floor[(p+1)/2] -1 = floor[(5+1)/2] -1 = 2; p= 5 from M5.

          Try another Norm... and see if I'm right. Imagine... a single test
          to determine the primality of Mp's! We can call it the Luhn-Bouris
          test for Mersennes. It can always be confirmed using the LL-test.
          Bill Bouris

          >
          > Example:
          >
          > M(13)=8191
          > R=5460
          > we found T=5929
          >
          > The idea is a consequence of the Lucas Lehmer Test.
          >
          >
          > regards
          >
          > Norman
          >
          >
          >
          > Lesen Sie Ihre E-Mails jetzt einfach von unterwegs.
          > www.yahoo.de/go
          >
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